This song is also known as “The Fly be on the Turmot”, not to be confused with a different song which starts:
The fly be on the turmot and the jumper’s on the hops.
Turmot is of course a dialect form of turnip and the dialect and mock rustic speech point to a stage origin of this song. Songs of the mock rustic type seem to have come into the English repertoire later in the 19th century and were taken up by country singers in spite of the crude parody of their speech and manners. No trace of this song can be found before it was published in 1893 by Broadwood and Maitland in English County Songs, when it was already well known in several counties and by the armed forces. Its rusticity has meant that its spread is confined to the southern and midland counties of England but no further. Several counties have claimed it for their own. Although the Roud index only shows a few instances of it being collected, I suspect that it was much wider known. Certainly Gloucestershire has had its share of versions. For a local version, see http://glostrad.com/fly-be-on-the-turmot-the/.